An inverse method of modeling thermal histories from apatite fission-track data

Abstract Apatite fission-track (FT) ages and track length distributions are important sources of information about the thermal histories of rocks. Recent advances in the understanding of track annealing in apatite provide a solution to the forward problem of predicting FT ages and track length distributions that result from a given thermal history. In this paper, a method is presented to address the inverse problem—estimation of the thermal history from FT data. The inverse method uses an iterative approach (the downhill simplex) to systematically modify a starting thermal history to achieve satisfactory statistical agreement between the predicted and observed FT age and track length distribution. However, because of analytical uncertainties, a unique thermal history does not exist. Monte Carlo simulations are used to take into account the uncertainties in the data and yield a spectrum of possible thermal histories. The results are based on the isothermal annealing model of Laslett et al. ([1], Chem. Geol. Isot. Geosci. Sect., Vol. 65) but because the method uses forward predictions and not an analytical formula specific to a single annealing model, alternative annealing models could be used within the same framework. This method is an improvement in interpreting fission-track data because the range of thermal histories permitted by the data can be evaluated. To demonstrate the method, it is applied to several sets of test data created by forward modeling of idealized thermal histories. The results show that the age at which the sample cooled through its closure temperature and the most general features of the thermal history are revealed. However, data from partially annealed samples have wide spectra that reflect large uncertainties in the form of the thermal history. For such samples, FT data alone are not likely to provide strong tests of geologic hypotheses. Conversely, geologic information may play a crucial role in constraining the thermal history spectrum. In application to uplift-related cooling, this inverse method can provide much more realistic assessments of the cooling rate and its uncertainty than are otherwise possible.